Forming Connections in Visualizing Quantitative Data: 3C – 9

objectives for this activity

During this activity, you will:

Click on a skill above to jump to its location in this activity.

In the previous section, What to Know About Visualizing Quantitative Data: 3C, you learned about two graphs used to display a quantitative variable, the histogram and the dotplot. In this activity, we’ll use these graphs to visualize the distribution of a single quantitative variable: movie runtimes.

A reel of film, a popcorn bucket, movie tickets, and a beverage cup.

At the end of the previous section, you were asked to record the runtime of your favorite movie. To prepare for this activity, think about your favorite movie and its runtime. How do you think the runtime of your favorite movie would compare to a list of runtimes of critically acclaimed movies? What do you think might be the typical length of a movie? 100 minutes? Longer? Shorter? Let’s get started in this activity by answering these questions below.

question 1

How long is your favorite movie?

question 2

Do you think other frequently viewed movies are generally under or over 100 minutes? Explain.

video placement

[Intro: What do you think? Do the runtimes of highly rated movies tend toward a certain length or not? To explore that question, we’ll look at a list of the top 100 movies from the review site Rotten Tomatoes. You are probably still getting used to the data analysis tool so let’s review briefly how to create a histogram and dotplot using technology. We’ll get started by going to the data analysis tool. [voice-over the tool]. We’ll select the Single Group tab and select “Your Own” under Enter Data and “Individual Observations.” We need to get the data from the spreadsheet. It’s embedded here, in Step 5. [download and open]. There are three variables here. We need the data for runtime so we’ll copy that and paste it into the tool. Let’s name the variable “Movie Runtime.” And we see our histogram has been created. I’ll just uncheck boxplot to get that out of the way. We can create a dotplot here as well. Your tool may have a default binwidth for the histogram that is different. Let’s choose 5.  The idea is to use the display to understand the distribution. What do you notice about it? What is the shortest runtime? What is the longest? You can take the difference between these values to get the range of the distribution. Which runtimes appear most often in the data? Do there appear to be any values that are unusual or extreme? What about this display makes it easy to understand about the distribution? What is less easy to see? Think about these questions as you move through the activity questions below.]

Visualizing Data Distributions

There are multiple ways to visualize the distribution of a quantitative variable such as movie runtime. Understanding that some features of a distribution are more apparent in some graphical displays than in others will help us to understand which display to use to answer which question about the distribution. In this case, we wondered if popular movies tend to be under or over 100 minutes long. We’ll need a dataset that includes runtime and a specific question to ask. Let’s examine different visual displays of movie runtimes from a real dataset to answer the question, “how long are highly rated movies, in general?”

To do so, we’ll look at the distribution of the runtime (in minutes) of the Rotten Tomatoes Top 100 Movies of all Time.[1] Using data from a spreadsheet, you will create two different graphical displays to visualize this distribution—a histogram and a dotplot.

First, let’s create a histogram. You may recall the steps to create a histogram from a spreadsheet in the data analysis tool that you used in the previous section, What to Know About Visualizing Quantitative Data: 3C.  The steps are provided below to help you as you continue to get used to the technology.

Go to the Describing and Exploring Quantitative Variables tool at https://istats.shinyapps.io/EDA_quantitative/ and create a histogram for the distribution of runtime of the top 100 highly rated movies as ranked by Rotten Tomatoes.

Step 1) Select the Single Group tab at the top of the screen.

Step 2) Locate the dropdown under Enter Data and select Your Own.

Step 3) For Do you have select Individual Observations.

Step 4) In the Name of Variable box, type “Movie Runtime”.

Step 5) Download the Movie Runtime spreadsheet and copy and paste the data in the runtime column.

Step 6) Locate Choose Type of Plot and choose Histogram. Unselect any other types.

Step 7) Under Select Binwidth For Histogram choose 5.

question 3

question 4

Write down 2 or 3 features of the distribution you observe from your histogram.

Now, let’s create a dotplot for comparison. In the same tool in which you have the histogram displayed, select Dotplot under Choose Type of Plot. This will create a dotplot for the distribution of runtime.

question 5

question 6

Write down 2 or 3 features of the distribution you observe from your dotplot.

question 7

What information seems easier to identify from the histogram? From the dotplot?

Compare and contrast features present in different graphical displays of quantitative data

The following are a few questions we’d like to answer about the runtimes of the highly rated movies. Answer each question and identify which graphical display(s) you find to be more helpful to answer Questions 8 – 11.

question 8

Are there any highly rated movies longer than 2 hours (120 minutes)? Which display was more helpful to answer this question?

question 9

How many highly rated movies are fewer than 100 minutes long? Which display was more helpful to answer this question?

question 10

How many highly rated movies are exactly 120 minutes? Which display was more helpful to answer this question?

question 11

Based on these data, is a highly rated movie more likely to be 100 minutes or 110 minutes? Which display was more helpful to answer this question?

Identify the most useful graphical display(s) to answer a given research question

Now consider all the questions, from 3 – 11, to compare and contrast the histogram and dotplot.

question 12

Discuss the pros and cons for each plot. Write down at least one pro and one con for each plot type.

question 13

Which plot type do you think is most useful for helping us visualize and understand the distribution of runtimes for the highly rated movies? Explain.

question 14

Suppose you wanted to visualize and understand the distribution of runtimes for 1,000 movies on IMDB. Which plot do you think is most useful for this analysis task? Explain. If your answer is different from Question 13, briefly explain why.

question 15

How did the runtime of your favorite movie compare to the distribution of the Top 100 Movies as ranked by Rotten Tomatoes?

video placement

[wrap-up: “How do you feel about quantitative distributions and their displays? Were the histogram and dotplot growing more familiar to you towards the end of the activity? Hopefully, you were able to see that each comes with its own advantages and disadvantages for displaying a quantitative variable. Histograms can provide a nice overview of range and how the variable values compare across the range of data but histograms hide finely detailed information about the data. Dotplots can give precise information about frequency appearing and unusual values but they become overwhelming and difficult to read with large datasets. Which display did you think would be better to visualize a dataset with 1,000 observations? Let’s take a look at the objectives for this activity. You’ve used technology to create both a histogram and a dotplot to display quantitative date. And you’ve compared and contrasted them to understand which situations are better suited for each. You’ll learn later that these are not the only ways to visualize a quantitative variable, but these are commonly used, and provided you practice using technology. In the next section, we’ll continue the exploration of quantitative variables by learning some statistical terms to use to describe their distributions: shape, center, and spread.”]

  1. “Top 100 Movies of All Time (All Genres).” Top 100 Movies of All Time - Rotten Tomatoes, https://www.rottentomatoes.com/top/bestofrt/. ↵